RRB NTPC CBT-I Official Paper (Held On: 22 Jan 2021 Shift 1) (Previous Year Paper)

Given

(√5 + √11) (√5 - √11)

Formula used

(a + b) (a - b) = a² - b²

Calculation

(√5)² - (√11)²

⇒5 - 11

⇒-6

∴ (√5 + √11) (√5 - √11) is - 6

The correct answer is Amritsar.

Key Points

• Amritsar was originally known as Ramdaspur.
• It was founded by the fourth Sikh Guru, Guru Ram Das, in 1577.
• The city is home to the Harmandir Sahib, also known as the Golden Temple, which is the holiest Gurdwara of Sikhism.
• Amritsar is a major cultural and religious center in the state of Punjab.

Additional Information

Given

Diameter of hemisphere = 7 cm

Formula used

Total surface area of hemisphere = 3πr²

r is radius respectively

Calculation

Radius of hemisphere, r = Diameter/2

⇒ 7/2

Total surface area of hemisphere = 3 × (22/7) × (7/2)²

⇒ 3 × (22/7) × 49/4

⇒ 3 × 22 × (7/4)

⇒ (3 × 11 × 7)/2

⇒ 231/2

⇒ 115.50 cm²

∴ Total surface area is 115.50 cm²

The correct answer is Indore.

Jantar Mantar refers to a collection of architectural astronomical instruments built in India.

Key Points

• Jantar Mantar locations are well known in Jaipur, Delhi, Varanasi, and Ujjain.
• Each location features uniquely designed instruments allowing observations of the celestial bodies with the naked eye.
• The Jantar Mantar in Jaipur is the largest and most famous, recognized as a UNESCO World Heritage site.

Additional Information

• The term Jantar Mantar is derived from Yantra, instruments for calculation, and Mantra, formula or in this context 'calculation.
• Indore does not have a Jantar Mantar, making it the correct answer for the city that does not possess such astronomical instruments.

Given

p² - 7p + 12

p = 3

Calculation

(3)² - 7 × 3 + 12

⇒ 9 - 21 + 12

⇒ - 12 + 12

⇒ 0

∴ The value of p2 - 7p + 12 is 0

Given

Sohan's speed = 3.5 km/h

Mohan's speed = 4 km/h

Distance = 1.5 km

Formula used

Time = Distance/Speed

when two objects move with s₁ and s₂ speed in the same direction, then final speed will be difference of their speed.i.e. (S₁ - S₂)

Calculation

Time = 1.5/(4 - 3.5)

⇒ 1.5/0.5

⇒ 3 hours

∴ Sohan and Mohan will take 3 hours to be 1.5 km apart if they start in the same direction.

The correct answer is Atomic Number.

Key Points

• Atomic Number is the number of protons in the nucleus of an atom.
• The Modern Periodic Table is arranged in order of increasing atomic number.
• This arrangement resolves anomalies present in Mendeleev's periodic table, which was based on atomic mass.
• Elements with similar properties recur at regular intervals or periods when arranged by increasing atomic number.

Additional Information

Shortcut Trick

Find the HCF of numerical coefficients: HCF(28, 70) = 14.

For variables, take the lowest power of each common base.

Lowest power of p is p³ and lowest power of q is q².

Combine them: 14 × p³ × q².

∴ The correct answer is 14 p³q².

Alternate Method

Given: First term = 28 p⁵q², Second term = 70 p³q⁴.

Formula: HCF = Product of the common prime factors with the smallest power.

⇒ Prime factorization of 28 = 2² × 7

⇒ Prime factorization of 70 = 2 × 5 × 7

⇒ HCF of (28, 70) = 2¹ × 7¹ = 14

⇒ Common variables are p and q.

⇒ Smallest power of p in both terms = p³

⇒ Smallest power of q in both terms = q²

⇒ Total HCF = 14 × p³ × q² = 14 p³q²

∴ The correct answer is 14 p³q².

Additional Information

LCM of Monomials

To find the LCM, take the highest power of each variable and the LCM of the coefficients.

HCF of Fractions

HCF = HCF of Numerators ÷ LCM of Denominators.

Product Rule

For any two numbers, Product of numbers = HCF × LCM.

The correct answer is Gulf of Kutch.

Key Points

• The Gulf of Kutch was declared as a Marine National Park by the Government of India in 1982 for marine conservation.
• It is located on the southern coast of the Kutch district in the state of Gujarat.
• The park is known for its rich marine biodiversity, including coral reefs, mangroves, and various species of fish and marine animals.
• It is the first Marine National Park in India, highlighting its importance in marine conservation efforts.

Additional Information

Given

64, 63, 62, 65, 67, 66 and 61

Concept

To find the median, arrange the data in ascending order

if n is odd number, n is number of observation

Median = [(n + 1)/2]th term

Calculation

Arrange the data in ascending order = 61, 62, 63, 64, 65, 66 and 67

Median = [(7 + 1)/2]th term

⇒ 4^th term

⇒ 64

∴ The median weight is 64 Kg.

The logic followed here is:

The double difference between the numbers is the multiples of 6.

Hence, the correct answer is 120**.**

The correct answer is Dr B R Ambedkar.

Key Points

• Dr B R Ambedkar was a prominent leader and social reformer but never presided over the Indian National Congress.
• Sarojini Naidu was the first Indian woman to become the President of the Indian National Congress.
• Surendranath Banerjee was one of the early leaders of the Indian National Congress and served as its President.
• Dada Bhai Naoroji was one of the founding members of the Indian National Congress and served as its President multiple times.

Additional Information

Given

(√5 + √7)²

Formula used

(a + b)² = a² + b² + 2ab

Calculation

(√5)² + (√7)² + 2 × √5 × √7

⇒ 5 + 7 + 2√35

⇒ 12 + 2√35

⇒ 2(6 + √35)

√35 is an irrational number.

so, (√5 + √7)² is a irrational number.

∴ (√5 + √7)² is a irrational number.

The logic followed here is:

In order to define the time period:

⇒  Days are combined to form Week.

⇒Week are combined to form a Month.

Similarly,

⇒ Months are combined to form Year. 

Hence, Year is related to the Month in the same way as Week is related to Day.

Hence, the correct answer is " Year".

The least possible Venn Diagram is as follows:

i) All colour-blinds are colourful. → False ( As some color blinds which are animals cannot be colorful).

ii) Some colour-blinds are animals. → True (As some animals are colour-blind then some colour-blind are animals will also be a definite statement).

iii) All colour-blinds are animals. → False (as All colourfuls are colour-blind but not animals.)

iv) Some animals are colourful. → False ( as All colourfuls are colour-blind but not animals.).

Hence, the correct answer is "Some colour-blinds are animals".

The statement gives an advertisement promoting pure and natural honey of company Z.

• Since it is promoting pure honey, it implies that artificial honey can be prepared. So, assumption I is implicit.
• Nothing about the pricing of pure or artificial honey has been stated, so assumption II is not implicit.

Hence the correct answer is option 2.

The correct answer is Pinterest.

Key Points

• Pinterest is primarily a visual discovery engine for finding ideas like recipes, home and style inspiration, and more.
• Unlike microblogging sites, Pinterest focuses on sharing images and visual content rather than text updates.
• Users create and share collections of visual bookmarks (called "pins") organized into themed boards.
• Microblogging sites like Twitter and Tumblr focus on short text posts and quick updates.

Additional Information

The correct answer is Sikhs.

Key Points

• The Adi Granth, also known as the Guru Granth Sahib, is the central religious scripture of Sikhism.
• It was compiled by Guru Arjan, the fifth Sikh Guru, in 1604.
• The Adi Granth is written in Gurmukhi script and includes hymns from Sikh Gurus and various other saints.
• It serves as a guide for Sikhs in their spiritual and daily lives.

Additional Information

The correct answer is Jaipur.

Key Points

• Jaipur is known for its grand celebration of the Elephant Festival.
• The festival is celebrated annually on the day of Holi.
• During the festival, elephants are decorated with vibrant colors, jewelry, and saddle cloth.
• Events like elephant parades, races, and tug-of-war are organized.
• The festival attracts a large number of tourists from all over the world.

Additional Information

The correct answer is Pampore.

Key Points

• Pampore is a town in the Pulwama district of Jammu and Kashmir, India.
• The town is famously known as the "Saffron town" due to its extensive saffron cultivation.
• Saffron from Pampore is considered one of the best in the world due to its high quality and distinct flavor.
• The cultivation of saffron in Pampore dates back to ancient times and is an integral part of the region's heritage.

Additional Information

Given

Marks got = 60

Failed by 60 marks

Minimum % to pass = 60

Calculation

let the maximum marks are x

According to question

60% of x = 60 + 60

⇒ 60x/100 = 120

⇒ x = (120 × 100)/60

⇒ x = 200

∴ Maximum marks is 200.

The correct answer is Spam.

Key Points

• Spam refers to unsolicited commercial emails that flood the Internet.
• These emails are often sent in bulk to a large number of recipients.
• Spam emails can contain advertisements, promotions, or fraudulent content.
• They can be annoying and may also pose security risks by containing malicious links or attachments.

Additional Information

The correct answer is Chlorine.

Key Points

• Chlorine is a greenish-yellow gas at room temperature.
• It has a characteristic pungent smell that is easily recognizable.
• Chlorine is commonly used in water purification and disinfectants.
• It is a highly reactive element and can form compounds with most other elements.

Additional Information

Given

Number of days taken by A to complete a work = 12

Number of days taken by B to complete a work =16

Concept

find the efficiency of the person

work = efficiency × time

Calculation

Total work(L.C.M of 12 and 16) = 48 units

Work done by A in one day = 48/12

⇒ 4 units

Work done by B in one day = 48/16

⇒ 3 units

Work done by A and B in two days(when work alternatively) = 4 units + 3 units

⇒ 7 units

work done by A and B in 12 days = 7 × 6

⇒ 42 units

work done on 13^th day = 42 + 4

⇒ 46 units

Remaining work = (48 - 46)units

2 units

work done by B of 2 units = 2/3 days

Total time taken by A and B when work alternatively is 13$2\over3$days.

∴ In 13$2\over3$ days the task be finished if they work for one day each alternatively, and A begins the work.

The correct answer is Child Vaccination.

Key Points

• Mission Indradhanush was launched by the Government of India in December 2014.
• The mission aims to cover all those children who are either unvaccinated or are partially vaccinated against seven vaccine-preventable diseases.
• The diseases targeted are Diphtheria, Pertussis, Tetanus, Polio, Tuberculosis, Measles, and Hepatitis B.
• The mission also aims to improve the coverage of vaccines in areas with low immunization rates.

Additional Information

The correct answer is Cinema.

Key Points

• The Dadasaheb Phalke Award is the highest recognition in the field of Indian cinema.
• It was instituted in 1969 by the Government of India.
• The award is named after Dadasaheb Phalke, who is considered the father of Indian cinema.
• Recipients of the award are honored for their outstanding contribution to the growth and development of Indian cinema.

Additional Information

The Dadasaheb Phalke Award includes a Swarna Kamal (Golden Lotus) medal, a shawl, and a cash prize.

The award is presented annually at the National Film Awards ceremony by the Directorate of Film Festivals, an organization set up by the Ministry of Information and Broadcasting.

Dadasaheb Phalke, whose full name was Dhundiraj Govind Phalke, made India’s first full-length feature film, Raja Harishchandra, in 1913.

The award has been given to many legendary figures in Indian cinema, including Raj Kapoor, Lata Mangeshkar, and Amitabh Bachchan.

The correct answer is 25^th January.

Key Points

• National Voters Day is celebrated on 25^th January every year in India.
• This day marks the foundation of the Election Commission of India in 1950.
• The celebration aims to encourage more young voters to participate in the political process.
• Various awareness programs and activities are organized to educate citizens about the importance of voting.

Additional Information

Given

Selling Price = Rs.31

Loss = 7%

Formula used

Profit = selling Price - cost Price

or 

cost price = selling price + loss

Calculation

let the cost price is Rs. x

x = 31 + 7% of x

⇒ x - 7% of x = 31

⇒ 93x/100 = 31

⇒ x = (31 × 100)/93

⇒ 100/3

Profit = 35 - (100/3)

⇒ (105 - 100)/3

⇒ 5/3

Profit % = [(5/3)/(100/3)] × 100

⇒ [(5/3) × (3/100)] × 100

⇒ 5%

∴ The profit percentage will be 5%, when he sells the same article at Rs. 35

The logic followed here is:

The value of $\sqrt {5}$ , $\sqrt {7}$  and $\sqrt {3}$  is an irrational number whereas, the value of $\sqrt {9}$ is a rational number.

 $\sqrt {5}$  = 2.236

 $\sqrt {7}$  = 2.646

 $\sqrt {3}$  = 1.732

 $\sqrt {9}$  = 3

Hence, $\sqrt {9}$ is the odd one among the given alternatives.

The correct answer is Chittaranjan Das.

Key Points

• Chittaranjan Das was a prominent Indian freedom fighter and political leader.
• He is popularly known as Deshbandhu, which means "Friend of the Nation".
• He played a significant role in the Non-Cooperation Movement against British rule.
• Das was also a leading figure in the Indian National Congress and was elected its president in 1922.

Additional Information

The correct answer is India Gate.

Key Points

• India Gate was built as a war memorial to soldiers of the undivided Indian Army who died during the First World War.
• It was designed by Sir Edwin Lutyens, a prominent British architect.
• The structure was completed in 1931 and stands at the eastern end of the Rajpath in New Delhi.
• The monument is inscribed with the names of over 13,000 servicemen who died in the First World War and the Third Anglo-Afghan War.

Additional Information

The logic followed here is:

All the numbers are written consecutively from bottom to top.

The numbers are written as follows:

12, 34, 56, 78, 910, and 1112.  

Hence, the question mark is replaced by 910.

Alternate MethodThe logic followed here is:

Step to be followed:

• 2 is added to the first digit of the number to obtain 1 digit of the next number.
• 2 is added to the second digit of the number to obtain the second digit of the next number.

For 12 and 34:

• 1 + 2 = 3
• 2 + 2 = 4
• = 34 which is next number

For 34 and 56:

• 3 + 2 = 5
• 4 + 2 = 6
• = 56 which is the next number

For 78 and missing number:

• 7 + 2 = 9
• 8 + 2 = 10
• = 910
• Thus missing number is 910

​Let's check if this logic followed in all:

For 910 and 1112:

• 9 + 2 = 11
• 10 + 2 = 12
• = 1112 which is our top number

Hence, the correct answer is "910".

The correct answer is Public school education for all.

Key Points

• Digital India is a flagship program launched by the Government of India to transform the country into a digitally empowered society and knowledge economy.
• The primary focus areas of the Digital India programme include universal access to mobile services, e-governance, and broadband highways.
• Public school education for all is not specifically mentioned as a growth area under the Digital India programme.
• The initiative aims to ensure that government services are made available to citizens electronically by improving online infrastructure and increasing internet connectivity.

Additional Information

The correct answer is P V Sindhu.

Key Points

• P V Sindhu is a renowned Indian badminton player.
• She was conferred the Padma Bhushan in 2020, which is India's third-highest civilian award.
• Sindhu has also been awarded the Padma Shri in 2015 and the Rajiv Gandhi Khel Ratna in 2016.
• She became the first Indian woman to win a silver medal in badminton at the 2016 Rio Olympics.

Additional Information

The Padma Bhushan is one of the highest civilian awards in India, given for distinguished service of a high order in any field.

The correct answer is Exosphere.

Key Points

• The Exosphere is the outermost layer of Earth's atmosphere.
• It has the lowest density of all the atmospheric layers.
• Particles in the exosphere are so sparse that they can travel hundreds of kilometers without colliding with one another.
• This layer gradually transitions into outer space, making it extremely thin.

Additional Information

Given:

The population of a town increases by 5% annually

The present population = 640000

Calculation:

According to the question:

The population of town in first year = (640000 × 5/100)

⇒ 32000

After first year, the population of town = (640000 + 32000)

⇒ 672000

Now,

The population of town in second year = (672000 × 5/100)

⇒ 33600

After second year, the population of town = (672000 + 33600)

⇒ 705600

∴ The population be in 2 years' time is 705600.

Given:

The mean of 20 observations = 22.5

One observation was wrongly noted as -25 instead of 25

Formula used:

Mean = sum of observations/Number of observations

Calculation:

The mean of 20 observations = (20 × 22.5)

⇒ 450

Now,

The correct sum = 450 – (-25) + 25

⇒ (475 + 25) = 500

The correct mean = (500/20)

⇒ 25

∴ The correct mean is 25.

The correct answer is USSR.

Key Points

• Five-Year Plans were first implemented in the USSR under Joseph Stalin in 1928.
• India adopted the concept of Five-Year Plans from the USSR to systematically plan its economic development.
• India's first Five-Year Plan was launched in 1951, focusing on agriculture and irrigation.
• The Planning Commission, established in 1950, was responsible for formulating and overseeing the Five-Year Plans in India.
• The Five-Year Plans aimed to achieve balanced economic growth and social justice in India.

Additional Information

Five-Year Plans are centralized and integrated national economic programs. They were first implemented in the USSR and later adopted by several countries, including India, to plan and manage their economic development effectively. The main objectives of these plans are to increase the overall economic productivity, reduce poverty, and promote social equity. India's Planning Commission, which was later replaced by the NITI Aayog in 2015, was responsible for creating these plans.

The correct answer is Nagpur.

Key Points

• The Central AGMARK Laboratory is located in Nagpur, India.
• It is responsible for quality control and certification of agricultural products under the AGMARK standards.
• AGMARK is a certification mark employed on agricultural products in India, assuring that they conform to a set of standards approved by the Directorate of Marketing and Inspection (DMI).
• The laboratory plays a crucial role in ensuring the quality and safety of agricultural products in the market.

Additional Information

AGMARK is a certification mark used on agricultural products in India, ensuring their quality and standardization. The term AGMARK is derived from 'Ag' for agriculture and 'mark' for certification.

The AGMARK standards cover a wide range of products including cereals, pulses, vegetable oils, fruits, and vegetables. These standards are framed and regulated by the Directorate of Marketing and Inspection (DMI), an attached office of the Ministry of Agriculture and Farmers Welfare.

The Central AGMARK Laboratory in Nagpur performs the analysis and testing of agricultural products to ensure they meet the required standards. This helps in maintaining the quality and reliability of agricultural commodities in the Indian market.

The AGMARK certification is crucial for exporting agricultural products, as it serves as a mark of quality assurance recognized internationally.

Given:

Spent by Rani = 6.25%

Expenditure amount of Rani = Rs. 75

Calculation:

According to the question:

Let the Total amount be x

⇒ 6.25% of x = 75

⇒ 6.25/100 × x = 75

⇒ 2.5/40 × x = 75

⇒ 2.5x/40 = 75

⇒ x/40 = 30

⇒ x = Rs. (40 × 30)

⇒ x = Rs. 1200

∴ The required amount saved by Rani is Rs. 1200.

The correct answer is Tim Berners-Lee.

Key Points

• Tim Berners-Lee invented HTML in 1990.
• HTML stands for HyperText Markup Language.
• It is the standard markup language for creating web pages.
• Tim Berners-Lee also developed the first web browser and web server.

Additional Information

The correct answer is Plants.

Key Points

• Biodegradable materials are those that can be broken down by natural processes, such as the action of microorganisms.
• Plants are organic materials that decompose naturally, returning nutrients to the soil.
• Biodegradation helps in reducing waste and environmental pollution.
• Non-biodegradable materials, like glass and polythene, persist in the environment for a long time, causing harm.

Additional Information

Given:

If a map of a city was drawn on a scale of 0.05 centimetre to kilometre

Calculation:

According to the question:

0.05 cm = 1 km

⇒ 1 km = 5/100 cm

Then,

⇒ 1 km² = 25/10000 cm²

Now,

8000 km² = (25/10000 × 8000) cm²

⇒ (25/10 × 8) cm²

⇒ 200/10 cm²

⇒ 20 cm²

∴ The required area is 20 cm².

The correct answer is Cancer.

Key Points

• Cyclone-30 is a particle accelerator developed by the Department of Atomic Energy (DAE).
• It is primarily used for the production of radioisotopes for medical applications.
• These radioisotopes are used in the diagnosis and treatment of cancer.
• It enables the production of isotopes like Fluorine-18, which is critical for PET scans in oncology.

Additional Information

Given:

The third proportion to 12 and 30

Formula used:

b² = ac

Calculation:

According to the question:

⇒ a/b = b/c

⇒ 12/30 = 30/c

⇒ 12c = (30 × 30)

⇒ 12c = 900

⇒ c = (900/12)

⇒ c = 75

∴ The third proportion is 75.

The correct answer is Canada.

Key Points

• The United Nations Security Council (UNSC) has five permanent members.
• The Permanent Members are: France, China, Russia, the United Kingdom, and the United States.
• Canada is not a Permanent Member of the UNSC.
• The Permanent Members have veto power over substantive resolutions.

Additional Information

The United Nations Security Council (UNSC) is one of the six principal organs of the United Nations (UN), charged with ensuring international peace and security, recommending the admission of new UN members to the General Assembly, and approving any changes to the UN Charter.

The UNSC is composed of 15 members: 5 permanent members and 10 non-permanent members elected for two-year terms by the General Assembly.

The Permanent Members were granted their status in recognition of their pivotal roles in the establishment of the UN after World War II.

The UNSC is the only UN body with the authority to issue binding resolutions to member states.

Concept used:

Irrational number - An irrational number is a type of real number which cannot be represented as a simple fraction.

Calculation:

According to the given option:

We clearly see that √17 comes between 3 and 5

∴ The required number is √17.

Shortcut Trick

The given ratio sin θ : cos θ = 5 : 12 implies tan θ = 5/12.

Using the standard Pythagorean triplet (5, 12, 13), where Perpendicular = 5 and Base = 12.

The Hypotenuse must be 13.

Since sin θ = Perpendicular / Hypotenuse, the value is 5/13.

∴ The correct answer is 5/13.

Alternate Method

Given: Ratio of sin θ to cos θ is 5 : 12.

Formula: tan θ = sin θ / cos θ and sin θ = P / H.

⇒ sin θ / cos θ = 5 / 12

⇒ tan θ = 5 / 12

⇒ Let Perpendicular (P) = 5k and Base (B) = 12k

⇒ Hypotenuse (H) = √(P² + B²)

⇒ H = √((5k)² + (12k)²) = √(25k² + 144k²)

⇒ H = √(169k²) = 13k

⇒ sin θ = P / H = 5k / 13k = 5/13

This corresponds to Option 2 as provided in the question.

∴ The correct answer is 5/13.

Additional Information

Pythagorean Triplets

Common sets of integers (a, b, c) that satisfy a² + b² = c² include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

Trigonometric Ratios

For an acute angle: sin θ = Opp/Hyp, cos θ = Adj/Hyp, and tan θ = Opp/Adj.

Fundamental Identity

The primary trigonometric identity is sin²θ + cos²θ = 1, which holds for any angle θ.

The correct answer is Meghalaya.

Key Points

• Nagaland, Sikkim, and Mizoram each have only one seat in the Lok Sabha. - Meghalaya has two seats in the Lok Sabha: Shillong and Tura. - The Lok Sabha is the lower house of India's bicameral Parliament. - Meghalaya is represented by two Members of Parliament due to its population and geographical considerations.

Additional Information

• The Lok Sabha is composed of representatives of the people, elected by direct election on the basis of adult suffrage. - The total number of seats in the Lok Sabha is 545, out of which 543 members are elected and 2 members are nominated by the President. - The Lok Sabha has a term of five years, after which it is automatically dissolved unless extended during a national emergency. - The Speaker of the Lok Sabha is responsible for the conduct of business in the house and maintaining order.

The correct answer is Provide Government jobs to socially backward women.

Key Points

• The Swadhar Greh Scheme aims to provide shelter, food, and clothing for women in distress.
• It offers legal aid to women to help them resolve their issues.
• The scheme provides support to enable women to start afresh.
• It does not specifically aim to provide government jobs to socially backward women.

Additional Information

The logic followed here is:

Given number set 2, 28, 48, 58, 128:

⇒ 2 → Prime Number

⇒ 28 → Composite Number

⇒ 48 → Composite Number

⇒ 58 → Composite Number

⇒ 128 → Composite Number

Thus, except for option 3, all the given numbers are composite numbers whereas option 3 which is 2 is a Prime Number.

Hence, the correct answer is "Option 3".

The correct answer is Hip bone.

Key Points

• The hip bone is formed by the fusion of three bones: the ilium, ischium, and pubis.
• These three bones fuse during late adolescence to form a single bone known as the os coxae or pelvic bone.
• The hip bone is a major component of the pelvic girdle and plays a crucial role in supporting the body’s weight during standing and walking.
• It also provides attachment points for muscles and ligaments involved in movement and stability.

Additional Information

The correct answer is Mumbai.

Key Points

• Location: Indira Gandhi Institute of Development Research (IGIDR) is located in Mumbai, Maharashtra.
• Establishment: It was established by the Reserve Bank of India in 1987.
• Objective: The institute's primary objective is to carry out research on developmental issues from a multi-disciplinary point of view.
• Academic Programs: IGIDR offers M.Sc. and Ph.D. programs in Development Studies.
• Campus: The campus is spread over 14 acres and provides various facilities including a library, computer center, and residential quarters.

Additional Information

Given:

Sita earns 25% more than Rahim

Calculation:

Let the earning of Rahim be 100%

Then,

Sita earns 25% more than Rahim = (100 + 25)%

⇒ 125%

Now,

Required percentage = Earning difference/Sita's earning × 100

⇒ (125 – 100)/125 × 100

⇒ 25/125 × 100

⇒ 20%

∴ The required percentage is 20%.

The correct answer is 22^nd April.

Key Points

• Earth Day is observed on 22^nd April each year.
• This day is celebrated worldwide to demonstrate support for environmental protection.
• The first Earth Day was celebrated on April 22, 1970.
• Earth Day events are coordinated globally by the Earth Day Network.
• Over 193 countries participate in Earth Day activities each year.

Additional Information

The correct answer is Bangalore.

Key Points

• Dr. K. Kasturirangan, former Chairman of ISRO, inaugurated the Human Space Flight Centre in Bangalore in 2019.
• The Human Space Flight Centre is responsible for the implementation of the Gaganyaan mission.
• The centre is located within the ISRO headquarters in Bangalore.
• The inauguration marks a significant step towards India's first manned space mission.
• The Gaganyaan mission aims to send Indian astronauts to space by 2022.

Additional Information

The logic followed here is:

Row 1:

• 4² = 16 → 1 + 6 = 7 = Middle number
• 7² = 49 → 4 + 9 = 13 = Last number

Row 2: 

• 5² = 25 → 2 + 5 = 7 = Middle number
• 72 = 49 → 4 + 9 = 13 = Last number

Similarly,

• 6² = 36 → 3 + 6 = 9 = Middle number
• 9² = 81 → 8 + 1 = 9 = Last number

​Hence, the correct answer is "Option 3".

Alternate Method

The logic followed here is:

Row 1: 7 + 13 = 20; 20 ÷ 4 = 5

Row 2: 7 + 13 = 20; 20 ÷ 5 = 4

Similarly, the resultant of row 3 should be 3

Row 3: 9 + ? = 18; 18 ÷ 6 = 3

Here the value of ? will be

18 - 9  = 9

Hence, 9 is the correct answer.

The correct answer is Chinese.

Key Points

• Chinese is one of the six official languages of the United Nations.
• The other official languages are Arabic, English, French, Russian, and Spanish.
• The use of these languages ensures effective communication within the UN.
• Official documents are translated into these languages for accessibility.
• Meetings are also interpreted in these six languages.

Additional Information

United Nations:

The logic followed here is:

Here, the difference between the numbers of the series are in increasing order. 

Hence, the correct answer will be 20.

Given:

The arithmetic mean of 16, 18, 15, 17, p and 14 = 17

Formula used:

Mean = sum of observations/Number of observations

Calculation:

According to the question:

The sum of mean = (16 + 18 + 15 + 17 + p + 14) = 80 + p

Now,

The correct mean = (80 + p)/6 = 17

⇒ 80 + p = 102

⇒ p = (102 – 80)

⇒ p = 22

∴ The required value of p is 22.

The correct answer is Rabindranath Tagore.

Key Points

• Rabindranath Tagore founded Visva Bharati in 1921.
• Visva Bharati was initially established as a center for culture with the motto "Yatra Visvam Bhavatyekanidam" which means "where the world makes a home in a single nest".
• Tagore envisioned the university as a place where the whole world could meet in a single nest.
• In 1951, Visva Bharati was declared a Central University.

Additional Information

Given:

y2 – √5y - y + √5 = 0

Calculation:

y2 – √5y - y + √5 = 0

⇒ y(y – √5) – 1(y – √5) = 0

⇒ (y – √5) or (y – 1) = 0

⇒ y = √5 or 1

∴ The required value is √5, 1

The logic followed here is:

Now analyzing the options:

i) HIKNR

ii) FGILP

iii) JKMPT

iv) EFGIK

Thus, EFGIK is not following the common pattern of +1, +2, +3, +4.

\Hence, ' EFGIK' is the odd one.

The least possible Venn Diagram is as follows:

i) Some birds are feathers. → True

ii) All wings are birds. → False (as it is possible but not definite)

iii) Some birds are wings and feathers. → True

iv) Some feathers are wings. → True

Hence, 'All wings are birds.' is NOT implicit in the statements.

The logic followed here is:

1 Centimetre × 100 = 1 Metre

Similarly,

1 Paisa × 100 = 1 Rupee

Hence, Rupee is the correct answer.

Given:

Let the original data be x₁ , x₂ , x₃ , . . . , xn.

Formula Used:

Arithmetic mean = (x₁ + x₂ + x₃ + . . . + xn) / n

Calculation:

⇒ If each entry is increased by 7, the new data becomes (x₁ + 7) , (x₂ + 7) , (x₃ + 7) , . . . , (xn + 7).

⇒ New arithmetic mean = [(x₁ + 7) + (x₂ + 7) + (x₃ + 7) + . . . + (xn + 7)] / n

⇒ New arithmetic mean = (x₁ + x₂ + x₃ + . . . + xn) / n + (7 + 7 + 7 + . . . + 7) / n

⇒ New arithmetic mean = Arithmetic mean + 7

Therefore, the correct option is 1.

Calculation:

1. All natural numbers together with zero are called integers.

2. There is no largest natural number.

3. There is no largest whole number.

4. 1 is the smallest natural number.

⇒ Statement 1 is false because integers also include negative numbers.

⇒ Therefore, the correct answer is option 1.

The correct answer is Auxin.

Key Points

• Auxins are a class of plant hormones that regulate various aspects of plant growth and development.
• They play a crucial role in the elongation of cells in shoots and are essential for the growth of plants.
• Auxins are involved in the regulation of plant organ formation and are key in processes like phototropism and gravitropism.
• They also help in the differentiation of cells and tissues, which is critical for the formation of roots and other organs.

Additional Information

Concept used:

Terminating decimal means a decimal that can be expressed in a finite number of figures or for which all figures to the right of someplace are zero.

Calculation:

Given options are:

$\frac{2}{7}$ ≈ 0.2857 (not continues)

$\frac{2}{9}$ ≈ 0.2222 (continues)

$\frac{2}{3}$ ≈ 0.6667 (continues)

$\frac{2}{5}$ = 0.4

Hence, $\frac{2}{5}$ has a terminating decimal representation. 

∴ $\frac{2}{5}$ among the following has terminating decimal representation.

The logic followed here is:

Similarly,

Hence, 'IKUS' is the correct answer.

Given:

One-sixth of a number exceeds its one-ninth by 100

Calculation:

Let the number be x

According to the question,

x/6 - x/9 = 100

⇒ (3x - 2x)/18 = 100

⇒ x/18 = 100

⇒ x = 1800

∴ The number is 1800

The correct answer is Right to profession.

Key Points

• Right to profession is not explicitly mentioned as a fundamental right in the Constitution of India.
• The Constitution guarantees the right to practice any profession, or to carry on any occupation, trade, or business under Article 19(1)(g), but it is not termed as "Right to profession."
• Right to freedom includes freedom of speech and expression, assembly, association, movement, residence, and the right to practice any profession.
• Right to equality guarantees equality before the law and equal protection of the laws.
• Right to freedom of religion ensures religious freedom and allows individuals to profess, practice, and propagate their religion.

Additional Information

Shortcut Trick

Find the HCF of 85 and 153 by identifying their common factors:

85 = 5 × 17

153 = 9 × 17

Thus, HCF = 17.

Equate the given expression to the HCF: 85x − 153 = 17 ⇒ 85x = 170 ⇒ x = 2.

∴ The correct answer is 2.

Alternate Method

Given:

The numbers are 85 and 153.

The HCF of 85 and 153 is expressible in the form 85x − 153.

Formula Used:

The Highest Common Factor (HCF) of two integers is the largest positive integer that divides both numbers without leaving a remainder.

Calculations:

Find the prime factorisation of both numbers:

⇒ 85 = 5 × 17

⇒ 153 = 3 × 3 × 17 = 3² × 17

Identify the common factor between 85 and 153:

⇒ Common Factor = 17

⇒ HCF(85, 153) = 17

According to the problem, the HCF is equal to 85x − 153:

⇒ 85x − 153 = 17

⇒ 85x = 17 + 153

⇒ 85x = 170

⇒ x = 170 ÷ 85

⇒ x = 2

∴ The correct answer is 2.

Additional Information

Highest Common Factor (HCF)

The HCF of two or more numbers is the greatest common divisor that divides each of them exactly without leaving any remainder.

HCF and LCM Relation

For any two positive integers a and b, the product of their HCF and LCM is equal to the product of the numbers: HCF(a, b) × LCM(a, b) = a × b.

Euclid's Division Algorithm

An efficient method to calculate the HCF of two integers by repeatedly expressing the larger number in terms of the smaller one using the division lemma (a = bq + r) until the remainder r becomes zero.

The correct answer is Article 29.

Key Points

• Article 29 of the Indian Constitution provides for the protection of interests of minorities.
• This article ensures that any section of citizens having a distinct language, script, or culture have the right to conserve the same.
• It also ensures that no citizen shall be denied admission into any educational institution maintained by the State or receiving aid out of State funds on grounds of religion, race, caste, language, or any of them.
• Article 29 is a key provision for safeguarding the cultural and educational rights of minorities in India.

Additional Information

The question asks whether or not electronic gadgets be welcome in examination halls.

• Argument I suggests that they should not be allowed since they can help in cheating. Cheating is an unacceptable offence. So, argument I is strong.
• Argument II suggests that since electronic gadgets are costly, they should not be kept outside. But, for that matter, other facilities for safe deposit can be made, the main concern would be if they are allowed in the examination hall. Thus, argument II is not strong.

Hence the correct answer is option 3.

The logic followed here is:

Given:

A = 26

• A → Opposite → Z → Positional Value = 26 (which is the given code)

T = 7

• T → Opposite → G → Positional Value = 7 (which is the given code)
• The alphabets are coded as per their positional value in reverse alphabetical order.

The code for AUTHENTIC will be as follows:

Here, the code for AUTHENTIC will be 266719221371824.

Hence, '266719221371824' is the correct answer.

Additional InformationShortcut to remember the reverse positional letters.

The correct answer is A natural resource is a gift of nature that is useful for mankind.

Key Points

• Natural resources are materials or substances occurring in nature which can be exploited for economic gain.
• They are classified into renewable and non-renewable resources.
• Examples of natural resources include water, air, soil, minerals, and forests.
• They play a crucial role in the sustenance of life and the functioning of ecosystems.
• Natural resources are essential for economic development and human well-being.

Additional Information

Shortcut Trick

Tangents drawn from an external point to a circle are always equal in length ⇒ SA = SB = 12 cm.

In triangle SAB, since SA = SB and the included angle ∠ASB = 60°, the triangle must be equilateral.

For any equilateral triangle, all sides are equal ⇒ AB = SA = SB = 12 cm.

∴ The correct answer is 12 cm.

Alternate Method

Given: Tangent SA = 12 cm and ∠ASB = 60°.

Formula Used: Length of tangents from an external point are equal; Sum of angles in a triangle = 180°.

⇒ In ΔSAB, SA = SB (Length of tangents from external point S are equal).

⇒ Since SA = SB, then ∠SAB = ∠SBA (Angles opposite to equal sides).

⇒ In ΔSAB, ∠ASB + ∠SAB + ∠SBA = 180°.

⇒ 60° + 2 × ∠SAB = 180°.

⇒ 2 × ∠SAB = 120° ⇒ ∠SAB = 60°.

⇒ Therefore, ∠SAB = ∠SBA = ∠ASB = 60°.

⇒ This implies ΔSAB is an equilateral triangle.

⇒ AB = SA = SB = 12 cm.

∴ The correct answer is 12 cm.

Additional Information

Tangent-Radius Property

The radius of a circle is always perpendicular to the tangent at the point of contact (∠OAS = ∠OBS = 90°).

External Point Tangents

The lengths of the two tangents drawn from an external point to a circle are equal (SA = SB).

Line Joining Center and External Point

The line joining the center of the circle to the external point (SO) bisects the angle between the two tangents (∠ASO = ∠BSO).

Given:

Reena and Jaya can complete a piece of work in 6 days

Jaya alone can complete it in 8 days

Concept used:

Total work = LCM of time of workers 

Calculation:

LCM of 6 and 8 = 24 i.e total work,

Efficiency of Reena and Jaya together = 24/6 = 4

Efficiency of Jaya = 24/8 = 3

So, efficiency of Reena = 4 - 3 = 1

So, Reena will take 24/1 = 24 days

∴ Required answer is 24 days

The correct answer is Godavari and Krishna.

Key Points

• The Pattiseema Lift Irrigation Project is designed to divert water from the Godavari River to the Krishna River.
• This project aims to utilize surplus water from the Godavari to address water scarcity in the Krishna basin.
• It is a key initiative to improve irrigation and water supply in Andhra Pradesh.
• The project is one of the first river interlinking projects in India.

Additional Information

The relation between Guava, Potato and Vegetables will be as follows:

All potatoes are vegetables.

No guava is vegetable.

The least possible Venn diagram is as follows:

Hence, the correct answer is "Option 2".

Given:

$0.\overline{23}$ + $0.\overline{22}$ 

Concept used:

$0.\overline{ab} = 0.ababab$

Calculation:

$0.\overline{23}$ + $0.\overline{22}$ 

⇒ 0.232323 + 0.222222

⇒ 0.454545

⇒ $0.\overline{45}$

∴ Required answer is $0.\overline{45}$